On SL(2)-actions without 3-dimensional orbits
On some reductive group actions on affine space II.
On spherical nilpotent orbits and beyond
We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s -groups. This yields a description of spherical...
On symmetric semialgebraic sets and orbit spaces
For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.
On the complicatedness of the pair (g,K).
On the Euler number of an orbifold.
On the geometry of conjugacy classes in classical groupes.
On the linearization of actions of linearly reductive groups.
On the Moment Map of a Multiplicity Free Action
The purpose of this note is to show that the Orbit Conjecture of C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff [BJLR1] is true. Another proof of that fact has been given by those authors in [BJLR2]. Their proof is based on their earlier results, announced together with the conjecture in [BJLR1]. We follow another path: using a geometric quantization result of Guillemin-Sternberg [G-S] we reduce the conjecture to a similar statement for a projective space, which is a special case of a characterization...
On the motive of a quotient variety.
We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.
On the Periods of Enriques Surfaces. II.
On the reflection representation in Springer's theory.
On the stability of subgroup actions on certain quasihomogeneous -varieties.
On the stratification of the moduli space of Mumford curves
On the zero set of semi-invariants for quivers
Optimal destabilizing vectors in some Gauge theoretical moduli problems
We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...
Orbifold-Hodge numbers of Hilbert schemes
Orbites de semi-groupes de morphismes réguliers et systèmes non linéaires en temps discret.
Orbits, Invariants, and Representations Associated to Involutions of Reductive Groups.
Orbits of the Weyl group and a theorem of DeConcini and Procesi